A Direct Dynamics Trajectory Study of F- + CH3OOH Reactive

Publication Date (Web): July 21, 2007 .... Paul M. Zimmerman , Diana C. Tranca , Joseph Gomes , Daniel S. .... Journal of the American Chemical Societ...
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A Direct Dynamics Trajectory Study of F- + CH3OOH Reactive Collisions Reveals a Major Non-IRC Reaction Path Jose´ G. Lo´ pez,† Grigoriy Vayner,† Upakarasamy Lourderaj,† Srirangam V. Addepalli,† Shuji Kato,‡ Wibe A. deJong,§ Theresa L. Windus,§ and William L. Hase*,† Contribution from the Department of Chemistry and Biochemistry, Texas Tech UniVersity, Lubbock, Texas 79409, Department of Chemistry and Biochemistry, UniVersity of Colorado, Boulder, Colorado 80309, and EnVironmental Molecular Science Lab, Pacific Northwest National Laboratory, Richland, Washington 99352 Received March 12, 2007; E-mail: [email protected]

Abstract: A direct dynamics simulation at the B3LYP/6-311+G(d,p) level of theory was used to study the F- + CH3OOH reaction dynamics. The simulations are in excellent agreement with a previous experimental study (J. Am. Chem. Soc. 2002, 124, 3196). Two product channels, HF + CH2O + OH- and HF + CH3OO-, are observed. The former dominates and occurs via an ECO2 mechanism in which F- attacks the CH3group, abstracting a proton. Concertedly, a carbon-oxygen double bond is formed and OH- is eliminated. Somewhat surprisingly this is not the reaction path, predicted by the intrinsic reaction coordinate (IRC), which leads to a deep potential energy minimum for the CH2(OH)2‚‚‚F- complex followed by dissociation to HF + CH2(OH)O-. None of the direct dynamics trajectories followed this path, which has an energy release of -63 kcal/mol and is considerably more exothermic than the ECO2 path whose energy release is -27 kcal/mol. Other product channels not observed, and which have a lower energy than that for the ECO2 path, are F- + CO + H2 + H2O (-43 kcal/mol), F- + CH2O + H2O (-51 kcal/mol), and F- + CH2(OH)2 (-60 kcal/mol). Formation of the CH3OOH‚‚‚F- complex, with randomization of its internal energy, is important, and this complex dissociates via the ECO2 mechanism. Trajectories which form HF + CH3OOare nonstatistical events and, for the 4 ps direct dynamics simulation, are not mediated by the CH3OOH‚‚‚Fcomplex. Dissociation of this complex to form HF + CH3OO- may occur on longer time scales.

1. Introduction

An important concept in chemical kinetics is the reaction path, often defined by the intrinsic reaction coordinate (IRC).1 This path connects stationary points on the potential energy surface (PES) and is determined by following steepest descent trajectories from saddle points to minima with the kinetic energy they acquire continuously removed.2 The reaction path model may be combined with statistical theories3 to make predictions concerning the kinetics of a chemical reaction. A question of considerable interest is how accurately IRCs and statistical theories identify the actual atomic-level mechanisms for chemical reactions. This is particularly important for post-transition state dynamics where, after passing a rate controlling transition state, the PES may have a “rough” landscape, with multiple potential energy minima, reaction pathways, low-energy barriers, etc., connecting the transition state to multiple product channels. For low-pressure gas-phase † ‡ §

Texas Tech University. University of Colorado. Pacific Northwest National Laboratory.

(1) Fukui, K. J. Phys. Chem. 1970, 74, 4161. (2) Ishida, K.; Morokuma, K.; Komornicki, A. J. Chem. Phys. 1977, 66, 2153. (3) Moylan, C. R.; Brauman, J. I. In AdVances in Classical Trajectory Methods, Vol. 2, Dynamics of Ion-Molecule Complexes; Hase, W. L., Ed.; JAI Press Inc.: Greenwich, CT, 1994; p 95. 9976

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conditions, where deactivating collisions are unimportant and the total energy is constant, the statistical model is RRKM theory,4 which may be used to predict the time spent in each potential energy minima and the probabilities for transitions between minima and forming products. For a reaction in solution or involving a macromolecule with many degrees of freedom, the statistical model assumes that there is rapid energy transfer forming a Boltzmann distribution so that transition state theory may be used to calculate the unimolecular lifetimes of intermediates and probabilities of forming products. Several chemical dynamics simulations have shown that for some reactions the post-transition state dynamics do not follow IRCs and, instead, the trajectories follow dynamical pathways. Such non-IRC dynamics was found for cyclopropyl radical ring opening,5 the OH- + CH3F f CH3OH + F- SN2 reaction,6 in 1,2,6-heptatriene rearrangement,7 and in the heterolysis rearrangement of protonated pinacolyl alcohol.8 In recent work nonIRC dynamics has been identified for H2CO and CH3CHO (4) Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics: Theory and Experiments; Oxford University Press: New York, 1996. (5) Mann, D. J.; Hase, W. L. J. Am. Chem. Soc. 2002, 124, 3208. (6) Sun, L.; Song, K.; Hase, W. L. Science 2002, 296, 875. (7) Debbert, S. L.; Carpenter, B. K.; Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 2002, 124, 7896. (8) Ammal, S. C.; Yamataka, H.; Aida, M.; Dupuis, M. Science 2003, 299, 1555. 10.1021/ja0717360 CCC: $37.00 © 2007 American Chemical Society

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Table 1. Geometries at Selected Stationary Points for the F- + CH3OOH Reactiona geometry CH3OOH‚‚‚F-

TS1

theory

RF-H4

RO2-H4

RO1-O2

θF-H4-O2

θC-O1-O2

RF-H1

RH1-C

RO1-O2

θF-H1-C

θC-O1-O2

MP2/6-311+G(d,p) DFT/6-31+G(d) DFT/6-31+G(d,p) DFT/6-311+G(d,p)

1.267 1.261 1.275

1.103 1.125 1.112

1.453 1.462 1.458

176.4 176.4 176.3

105.8 106.8 107.0

1.246 1.272 1.297 1.345

1.305 1.303 1.278 1.247

1.613 1.686 1.642 1.630

173.6 170.2 170.3 170.3

110.6 110.8 110.8 110.4

CH2(OH)2‚‚‚F-

TS2

MP2/6-311+G(d,p) DFT/6-31+G(d) DFT/6-31+G(d,p) DFT/6-311+G(d,p)

RF-H1

RH1-C

RO1-O2

θF-H1-C

θC-O1-O2

RF-H4

RO2-H4

RC-O2

θF-H4-C

θO1-C-O2

1.776 1.749 1.729 1.730

1.114 1.122 1.124 1.122

1.453 1.464 1.465 1.462

166.9 168.1 168.7 167.9

109.0 109.6 109.6 109.9

1.595 1.595 1.614

1.001 1.010 1.005

1.403 1.407 1.405

154.1 154.3 153.8

112.5 112.7 112.8

HF + CH2O + OH-

F-‚‚‚CH3OOH

MP2/6-311+G(d,p) DFT/6-31+G(d) DFT/6-31+G(d,p) DFT/6-311+G(d,p) exptc

RF-H1

RH1-C

RO1-O2

θF-H1-C

θC-O1-O2

1.709 1.647 1.605 1.607 -

1.125 1.142 1.150 1.148 -

1.471 1.495 1.501 1.503 -

168.3 167.0 167.5 167.2 -

107.5 109.0 109.2 109.3 -

RH-F

b RO-H

RC-O

RC-H

θH-C-H

0.917 0.938 0.928 0.922 0.917

0.965 0.975 0.970 0.966 0.964

1.213 1.209 1.210 1.202 1.203

1.105 1.109 1.108 1.108 1.101

116.1 116.3 116.2 115.9 116.2

a Bond lengths are in angstroms (Å), and angles are in degrees (deg). b Bond length for OH-. c The experimental geometries of HF, OH-, and CH O are 2 from refs 50, 51, and 52, respectively.

dissociation via the C-H bond rupture channel.9-11 The dissociating H-atom crosses a ridge on the PES and “falls” into the highly exothermic elimination dissociation channel forming H2 from H2CO and CH4 from CH3CHO. Non-IRC dynamics for such a “roaming H-atom” mechanism was also observed in earlier studies of H-atom transfer.12,13 It is also noteworthy that non-IRC dynamics has also been identified and explained for the H + HBr f H2 + Br and O(3P) + CH3 f H2 + H + CO reactions.14,15 Non-IRC and non-TS dynamics are prevalent in high-energy collisions, where the reactive system traverses regions of the PES far above potential minima, IRCs, and TSs.16,17 In recent experiments, Kato and co-workers studied the 300 K kinetics of the base-mediated decomposition reaction F- + CH3OOH.18 Much to their surprise, the reaction did not yield the most exothermic products HF + CH2(OH)O- and the products predicted by the IRC. Instead, the much higher energy non-IRC products HF + CH2O + OH- were formed. In the work presented here the results of a B3LYP/6-311+G(d,p) direct dynamics simulation are reported, which probe the posttransition state dynamics for the F- + CH3OOH reaction. The results of the simulation agree with the previous experimental study and provide an atomic level understanding of the nonIRC dynamics.6,17 (9) Townsend, D.; Lahankar, S. A.; Lee, S. K.; Chambreau, S. D.; Suits, A. G.; Zhang, X.; Rheinecker, J.; Harding, L. B.; Bowman, J. M. Science 2004, 1158. (10) Lahankar, S. A.; Chambreau, S. D.; Townsend, D.; Suits, F.; Farnum, J.; Zhang, X.; Bowman, J. M.; Suits, A. G. J. Chem. Phys. 2006, 125, 044303. (11) Houston, P. L.; Kable, S. H. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 16079. (12) ter Horst, M. A.; Schatz, G. C.; Harding, L. B. J. Chem. Phys. 1996, 105, 558. (13) Troya, D.; Gonza´lez, M.; Wu, G.; Schatz, G. C. J. Phys. Chem. A 2001, 105, 2285. (14) Pomerantz, A. E.; Camden, J. P.; Chiou, A. S.; Ausfelder, F.; Chawla, N.; Hase, W. L.; Zare, R. N. J. Am. Chem. Soc. 2005, 127, 16368. (15) Marcy, T. P.; Dı´az, R. R.; Heard, D.; Leone, S. R.; Harding, L. B.; Klippenstein, S. J. J. Phys. Chem. A 2001, 105, 8361. (16) Meroueh, S. O.; Wang, Y.; Hase, W. L. J. Phys. Chem. A 2002, 106, 9983. (17) Yan, T.; Doubleday, C.; Hase, W. L. J. Phys. Chem. A 2004, 108, 9863. (18) Blanksby, S. J.; Ellison, G. B.; Bierbaum, B. V.; Kato, S. J. Am. Chem. Soc. 2002, 124, 3196.

2. Ab Initio Energies and Potential Energy Surface

2.1. Stationary Point Properties. CBS-QB3, MP2, and B3LYP theories were used to calculate the geometries and frequencies of the reactants, transition states, intermediates, and products of the F- + CH3OOH reaction. The structures and energies were calculated using the 6-311+G(d,p) basis set at the MP2 level of theory and the 6-31+G(d), 6-31+G(d,p) and 6-311+G(d,p) basis sets at the B3LYP level of theory. Vibrational frequencies were calculated at the MP2 and B3LYP levels of theory. 2.1.1. Geometries. The geometries at selected stationary points, optimized with the MP2 and B3LYP theories and different basis sets, are listed in Table 1 and depicted in Figure 1. Overall, the geometries calculated at the different levels of theory are in good agreement. The largest difference between the geometries, of the B3LYP/6-311+G(d,p) method used for the simulations and those for the MP2/6-311+G(d,p) method, is for the F-H1 bond length of F-‚‚‚CH3OOH and TS1. For the F-‚‚‚CH3OOH complex the B3LYP value of the F-H1 bond length is 0.1 Å shorter than that of MP2 theory. This difference is reversed for the TS1 transition state for which the B3LYP value is 0.1 Å larger. 2.1.2. Vibrational Frequencies. Vibrational frequencies were calculated for TS1, TS2, the F-‚‚‚CH3OOH complex, and the HF + CH2O + OH- products with the MP2 and B3LYP levels of theory and the 6-311+G(d,p) basis set and are listed in Table 2. These calculations were used to compare MP2 and B3LYP frequencies and to compare them with experiments. Overall the MP2 and B3LYP frequencies are in quite good agreement, with the largest difference for the O-O stretch of F-‚‚‚CH3OOH, i.e., 697 and 813 cm-1 for B3LYP and MP2, respectively. The frequencies of the HF + CH2O + OH- products, given by the B3LYP/6-311+G(d,p) theory used for direct dynamics simulations, are in excellent agreement with experiment, with an average difference less than 2%. It is of interest that TS2 has higher frequencies than TS1. As discussed below, in section J. AM. CHEM. SOC.

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Figure 1. Geometries at selected stationary points, for the F- + CH3OOH reaction, optimized with the B3LYP/6-311+G(d,p) level of theory. (a) CH3OOH‚‚‚F-, (b) TS2, (c) F-‚‚‚CH3OOH, (d) TS1, (e) CH2(OH)2‚‚‚F-, and (f) CH2O. Bond lengths in Å. The (‚‚‚) identifies noncovalent interactions.

4.4, this has a significant effect on the unimolecular rate constants for F-‚‚‚CH3OOH via TS1 and TS2 decomposition. 2.1.3. Energies. The CBS-QB3 energies were chosen as a benchmark for the accuracy of the calculations and were compared with energies calculated at the MP2 and B3LYP levels of theory. The resulting energies are listed in Table 3 and show that B3LYP theory gives a better accuracy than does MP2. According to experimental observations for this reaction,18 the major reaction channel leads to the formation of HF + CH2O + OH- via the transition state TS1. For this reaction pathway, B3LYP/6-311+G(d,p) gives a precision within 2 kcal/mol, while B3LYP/6-31+G(d,p), although good in most cases, results in a precision within 4 kcal/mol. Taking this into consideration, B3LYP/6-311+G(d,p) was chosen as most practical to perform the direct dynamics calculations of the F- + CH3OOH reaction. The stationary point potential energies for the F- + CH3OOH reaction pathways, at the chosen level of theory, are depicted in Figure 2. The difference in the B3LYP/6-311+G(d,p) and CBS-QB3 stationary point energies vary from 0.2 to 3.2 kcal/ mol with the largest value of 3.2 kcal/mol for HF + CH3OO-, CH2(OH)2‚‚‚F-, and F- + CO + H2 + H2O. 2.2. Intrinsic Reaction Coordinate Calculation. The IRC connecting the transition state TS1 and the products was calculated at the B3LYP/6-311+G(d,p) level of theory. Energies and geometries along the IRC(s) are shown in Figure 3. The term s identifies the value of the reaction coodinate. The initial IRC involves H-F and O-H bond formation after rupture of the H-C and O-O bonds to form a tight HF‚‚‚CH2O‚‚‚HOcomplex. For s between 2 and 5 amu1/2 Bohr, the IRC has a region with a less negative slope that involves OH- motion away from CH2O and rotation of this latter fragment. This rotation allows the migration of OH- and HF toward the carbon and oxygen atoms of CH2O, respectively, and a significant energy decrease. At an s of about 10 amu1/2 Bohr, the IRC shows a complete relocation of the OH- and HF fragments to form HO‚‚‚C2O-‚‚‚HF followed by the formation of HOCH2O-‚‚‚HF and, subsequently, HOCH2OH‚‚‚F-. At this point, the IRC enters an extremely shallow region in which the H‚‚‚F end of the 9978 J. AM. CHEM. SOC.

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HOCH2OH‚‚‚F- moiety slowly rotates toward OH to finally form the CH2(OH)2‚‚‚F- complex, which as illustrated in Figure 2 may dissociate to HF + CH2(OH)O- or CH2(OH)2 + F-. 3. Procedure for the Direct Dynamics Simulations Ab initio direct dynamics trajectory calculations,19-21 at the B3LYP/ 6-311+G(d,p) level of theory, were performed to investigate the dynamics of the F- + CH3OOH reaction. Comparisons with other levels of theory, as described in section 2.1, show that the chosen level of theory is the most feasible for the simulations. The general chemical dynamics program VENUS,22 interfaced with the electronic structure theory software package NWChem-4.7,23 was used for the simulations. 3.1. Initial Conditions. The direct dynamics trajectories were initiated for the F- + CH3OOH reactants, the TS1 transition state, and the HOCH2O-‚‚‚HF IRC region of the potential energy surface and terminated after 4 ps or when the separation between the reaction products exceeded 16 Å. Quasiclassical sampling,24 which includes zeropoint energy, was used to select initial coordinates and momenta for the trajectories. The F- + CH3OOH trajectories were started at an initial 15 Å separation between F- and the center of mass of CH3OOH. The attractive potential is -0.21 kcal/mol at this separation for the most favorable CH3OOH‚‚‚F- interaction. On the other hand, for this separation and the most favorable F-‚‚‚CH3OOH interaction, the attractive potential is smaller and -0.13 kcal/mol. The reaction (19) Bolton, K.; Hase, W. L.; Peslherbe, G. H. In Modern Methods for Multidimensional Dynamics Computations in Chemistry; Thompson D. L., Ed.; World Scientific: Singapore, 1998; p 143. (20) Sun, L.; Hase, W. L. In ReViews in Computational Chemistry, Vol. 19; Lipkowitz, K., Larter, R., Cundari, T. R., Eds.; Wiley: New York, 2003; p 79. (21) Hase, W. L.; Song, K.; Gordon, M. S. Comput. Sci. Eng. 2003, 5, 36. (22) Hase, W. L.; Duchovic, R. J.; Hu, X.; Komornicki, A.; Lim, K. F.; Lu, D. H.; Peslherbe, G. H.; Swamy, S. R.; Vande Linde, S. R.; Varandas, A.; Wang, H.; Wolf, R. J. Quantum Chemistry Program Exchange (QCPE) Bulletin 1996, 16, 671. (23) (a) Apra`, E., et al. NWCHEM, a computational chemistry package for parallel computers, version 4.7; Pacific Northwest Laboratory: Richland, WA 99352, 2005. (b) Kendall, R. A.; Apra`, E.; Bernholdt, D. E..; Bylaska, E. J.; Dupuis, M.; Fann, G. I.; Harrison, R. J.; Ju, J.; Nichols, J. A.; Nieplocha, J.; Straatsma, T. P.; Windus, T. L.; Wong, A. T. Comput. Phys. Commun. 2000, 128, 260. (24) Peslherbe, G. H.; Wang, H.; Hase, W. L. In AdVances in Chemical Physics, Vol. 105, Monte Carlo Methods in Chemical Physics; Ferguson, D. M., Siepman, J. I., Truhlar, D. G., Eds.; Wiley: New York, 1999; p 171.

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Table 2. Harmonic Frequencies of Selected Stationary Points for the F- + CH3OOH Reactiona mode

MP2/6-311+G(d,p)

DFT/6-311+G(d,p)

F- stretch F- bend CH3 torsion OOC wag OOH wag COO bend OO stretch CO stretch CH3 rock OOH rock CH3 deformation CH3 stretch OH stretch

TS2 204i 85 163 220 298 508 836 1009 1182, 1209 1335 1489, 1520, 1567 2799, 3082, 3154 3813

193i 90 183 248 315 490 821 940 1152, 1189 1326 1456, 1494, 1532 2646, 3001, 3084 3752

F- bend OOH wag F- stretch CH3 torsion COO bend OO stretch CO stretch CH3 rock OOH rock CH3 deformation CH3 stretch OH stretch

F-‚‚‚CH3OOH 89, 95 94, 104 167 136 202 225 426 428 469 465 813 697 995 940 1208, 1214 1179, 1189 1310 1262 1513, 1526, 1533 1459, 1487, 1499 2654, 3058, 3109 2336, 2973, 3020 3838 3778 TS1

F- stretch OOH wag F- bend COO bend OO stretch CH3 torsion CO stretch OOH rock CH3 rock CH3 deformation CH3 stretch OH stretch HF stretch OH stretch CH2 wag CH2 rock CH2 bend CO stretch CH2 symmetric stretch CH2 asymmetric stretch

exptb

461i 96 116, 131 325 558 585 1007 1090 1057, 1204 1310, 1414, 1490, 1523 2981, 2937 3808

and CH3OOH leads to collisions and chemical reactions with large b and, thus, large angular momentum. A smaller ensemble of trajectories was also initiated at the TS1 transition state, which links the F- + CH3OOH reactants with the products formed by F- interacting with the CH3- group of CH3OOH. The trajectories were initiated at TS1 with a 300 K rotational angular momentum distribution. The angular momenta for this distribution are much lower than those which result from F- + CH3OOH reactive collisions at large impact parameters, and it is of interest to see if the much lower 300 K rotational angular momentum affects the reaction dynamics. The initial conditions also included a 300 K energy distribution in reaction coordinate translation and a microcanonical ensemble of states for the vibrational modes orthogonal to the reaction coordinate. The energy for this ensemble corresponds to the reactant’s 300 K thermal energy plus the potential energy difference between the reactants and TS1, i.e., 11.5 kcal/mol. A small set of trajectories, initiated along the IRC, were also studied. Their initial IRC structure is HOCH2O-‚‚‚HF and identified by the dot in Figure 3. Initial conditions for the modes orthogonal to the IRC were sampled for a microcanonical ensemble, with an energy equal to the reactant’s thermal energy plus the potential energy difference between the reactants and HOCH2O-‚‚‚HF structure. The reaction coordinate translation and external rotation energies were sampled from 300 K Boltzmann distributions. 3.2. Maximum Collision Impact Parameter for the F- + CH3OOH Reaction. The collision impact parameter for each F- + CH3OOH trajectory was randomly selected from zero to bmax. To assist in the evaluation of bmax the capture model25 was used to estimate its value. This model is based on the effective potential

Veff(R) ) V(R) +

HF + CH2O + OH4199 3838 1206 1278 1559 1762 2976

4097 3755 1198 1259 1531 1814 2886

4138 3738 1191 1299 1529 1778 2978

3047

2944

2997

a Frequencies are in units of cm-1. b The experimental harmonic frequencies of HF, OH-, and CH2O are from refs 50, 51, and 53, respectively.

dynamics following this latter attractive interaction is the principal focus of this work, and the small attractive potential indicates it is appropriate to use an initial separation of 15 Å. The initial separation would need to be increased substantially to significantly decrease the reactants’ attractive interaction, and this would have a deleterious effect on the computational expense of the direct dynamics trajectories (see below). Initial conditions for the CH3OOH vibrational and rotational degrees of freedom were selected from their 300 K Boltzmann distributions. The initial relative translational energy Erel equalled 0.89 kcal/mol, i.e., the average value of Erel at the 300 K temperature of the F- + CH3OOH experiments.18 The collision impact parameter b was chosen randomly between zero and bmax (see discussion in the following section for the identification of bmax), and CH3OOH had a random orientation with respect to F-. The probability of a collision with a particular value of b is proportional to b, and the long-range interaction between F-

µRb2Vrel2 2R2

(1)

where R is the distance between F- and the center of mass of CH3OOH, V(R) is the reactants’ interaction potential, µR is the F- + CH3OOH reduced mass, b is the collision impact parameter, and Vrel is the relative translational velocity. V(R) was determined by assuming an equilibrium configuration for CH3OOH and locating F- along the C-H1 bond line, as illustrated in Figure 4. Values of V(R) were calculated at the B3LYP/6-311+G(d,p) level of theory used for the simulations, and Vrel was determined from the average relative translational energy at 300 K. Following the criterion for the capture model, bmax is the value of b for which the maximum of Veff(R) equals the initial relative translational energy Erel. For Erel ) 0.89 kcal/mol used in the simulations, the resulting bmax is 11.3 Å. This bmax was used as a guide in choosing the actual value for the simulations. Sets of 10 F- + CH3OOH trajectories were calculated at different values of b to determine the probability of F- interacting attractively with CH3OOH instead of directly scattering. For a b of 7.5 Å and less the probability of this attractive interaction is unity. However, for b in the range of 9.0-9.5 Å the combined probability for this attractive interaction is 0.06. For b ) 10 Å each of the trajectories scattered directly, without an attractive interaction, and bmax was set to 10 Å for the F- + CH3OOH simulations. 3.3. Trajectory Integration and Analysis. The trajectories were integrated using a Hessian-based predictor corrector algorithm26 and implemented in the development version of VENUS/NWChem. The total energy was conserved to within 0.01 kcal/mol. The wall computer processing time for a single trajectory integrated for 4 ps required 5.7 days on a dedicated 3.2 GHz Xeon dual-processor with 4 GB RAM. (25) Su, T.; Bowers, M. T. In Gas Phase Ion Chemistry, Vol. 1; Bowers, M. T., Ed.; Academic: New York, 1978; p 84. (26) Lourderaj, U.; Song, K.; Windus, T. L.; Zhuang, Y.; Hase, W. L. J. Chem. Phys. 2007, 126, 044105. J. AM. CHEM. SOC.

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ARTICLES Table 3. Electronic Structure Theory Energies for Stationary Points on the F- + CH3OOH PESa MP2

DFT(B3LYP)

structure

ZPEb

CBS-QB3

6-311+G(d,p)

6-31+G(d)

6-31+G(d,p)

6-311+G(d,p)

HF + CH3OOCH3OOH‚‚‚FTS2 F-‚‚‚CH3OOH TS1 CH2(OH)2‚‚‚FHF + CH2O + OHF- + CO + H2 + H2O F- + CH2O + H2O F- + CH2(OH)2 HF + CH2(OH)O-

-2.5 -0.3 -0.1 -0.6 -3.1 2.7 -6.8 -4.0 1.3 -

1.7 -38.0 -12.2 -15.4 -10.5 -108.0 -28.8 -46.0 -50.7 -61.6 -

5.8 -36.0 -10.5 -13.8 -9.7 -110.9 -35.2 -55.6 -57.6 -66.1 -

7.6 -11.7 -15.3 -12.7 -17.8 -44.6 -

5.9 -36.8 -12.1 -15.9 -14.6 -103.3 -22.8 -37.9 -47.7 -

4.9 -36.5 -12.4 -16.2 -11.5 -104.8 -26.9 -42.8 -51.0 -59.7 -63.4

a Energies (kcal/mol) are with respect to F- + CH OOH and do not include zero-point energy (ZPE). b Zero-point energy with respect to that for F- + 3 CH3OOH and calculated at the B3LYP/6-311+G(d,p) level of theory. With this ZPE included the CBS-GB3 energy for HF + CH3OO- is -0.8 kcal/mol.

Figure 2. Energy diagram for the F- + CH3OOH reaction at the B3LYP/6-311+G(d,p) level of theory. The energies shown are in kcal/mol and are relative to the F- + CH3OOH reactant channel. Zero-point energies are not included.

Figure 4. F- + CH3OOH system for the calculation of bmax using the capture model. The dot indicates the position of the CH3OOH center of mass, and the dashed line, the C-H1 bond line along which F- is located.

4. Results and Discussion Figure 3. Potential energy along the IRC connecting the transition state TS1 and CH2(OH)2‚‚‚F- potential energy minimum. s is the distance along the IRC. The dot identifies the HOCH2O-‚‚‚HF structure on the IRC, used to initiate some of the trajectories (see section 4.3). The potential energy at this point is -67 kcal/mol, with respect to the zero of energy for TS1.

The trajectories were analyzed for different types of events. The statistical uncertainty given, for the probability of a particular type of event, is 1 standard deviation (68% confidence level).27 (27) Truhlar, D. G.; Muckerman, J. T. In Atom-Molecule Collision Theory: a Guide for the Experimentalist; Bernstein R. B., Ed.; Plenum Press: New York, 1979; p 505. 9980 J. AM. CHEM. SOC.

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4.1. Dynamics of the F- + CH3OOH Collisions. 200 trajectories were propagated in order to investigate the F- + CH3OOH collision dynamics. Initial conditions were chosen for the trajectories as described above. The initial relative translational energy Erel is 0.89 kcal/mol, the average relative translational energy for the 300 K temperature of the experiments.18 Table 4 shows the number of trajectories for the different reaction channels found for the F- + CH3OOH collisions. 23% formed HF + CH2O + OH-, the major product reaction channel observed in the experiment,18 48% became trapped in the CH3OOH‚‚‚F- potential energy well and formed a reaction intermediate that lasted up to the 4 ps of the trajectory

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Table 4. Total Number of Trajectories for the Different Product Channelsa number of trajectories product

initiated at F- + CH3OOHb

initiated at TS1c

initiated at HOCH2O-‚‚‚HFd

HF+CH3OOCH3OOH‚‚‚FHF+CH2O+OHCH2(OH)2‚‚‚FF- + CH3OOH minor products

3 97 45e 0 55 0

0 0 76 0 0 4

0 0 5 0 0 0

a The trajectories are initiated in the reactant, TS1, and HOCH O-‚‚‚HF 2 regions of the F- + CH3OOH potential energy surface. b 200 trajectories c were initiated at the reactant channel. 80 trajectories were initiated at TS1. d Five trajectories were initiated at the HOCH O-‚‚‚HF structure along the 2 IRC. e Three of these events occurred by first forming the CH3OOH‚‚‚Fcomplex.

integration, 1.5% formed the HF + CH3OO- reaction products, and the remaining trajectories went back to the reactants. None of the trajectories formed the IRC complex. The large fraction of trajectories trapped in the CH3OOH‚‚‚F- potential energy well arises from the high-energy barriers between this complex and the HF + CH3OO- products and the F-‚‚‚CH3OOH complex. The long lifetime for CH3OOH‚‚‚F- is consistent with RRKM theory, as described in section 4.4. As discussed below in section 4.5, the fact that none of the trajectories followed the IRC is consistent with the experimental study.18 The IRC complex and its dissociation products comprise, at most, only 2% of the total experimental product yield. 4.1.1. HF + CH2O + OH- Products. The vast majority of the trajectories that formed HF + CH2O + OH- followed the pathway depicted in Figure 5. The observation of this pathway provides theoretical evidence for the elimination mechanism proposed by Kato and co-workers18 for base-mediated heterolytic decomposition of small alkyl hydroperoxides. Figure 5 clearly shows the association of the anion with an R-hydrogen (Figure 5b), crossing of the TS1 barrier (Figure 5c), and rupture of the C-H and O-O bonds (Figure 5d) to form formaldehyde, OH-, and HF (Figure 5e). About 1.5 ps were required for the system to move from the reactants to the TS1 barrier, and an additional 0.7 ps was required to reach the 16 Å separation between the HF + CH2O + OH- reaction products. Only a small fraction of the trajectories (1.5%) entered the CH3OOH‚‚‚Fpotential well and then escaped through transition state TS2 to follow the pathway shown in Figure 5. Comparison with the IRC, described above, shows that the trajectories that form HF + CH2O + OH- initially follow the IRC path up to s ∼5 amu1/2 Bohr. The dynamics of the trajectories show rupture of the H-C and O-O bonds after crossing the TS1 region, formation of a tight HF‚‚‚CH2O‚‚‚HOcomplex, and rotation of the CH2O fragment. However, the dynamics leads to the separation of OH- and HF from CH2O instead of allowing formation of the HO‚‚‚CH2O-‚‚‚HF IRC structure. The trajectories cease to follow the IRC when the slope of potential energy versus s becomes more negative at s ∼5 amu1/2 Bohr. A two-dimensional contour diagram of the post-transition state potential energy surface, following motion from TS1, is illustrated in Figure 6. Q1 represents the concerted movement of HF and OH- away from CH2O, and Q2 represents the inplane rotational motion of CH2O. Also depicted in Figure 6 is the IRC and the motion for a representative trajectory. The

Figure 5. Representative trajectory showing the reaction pathway from the reactants to the major product channel HF + CH2O + OH- at (a) 990 fs, (b) 1086 fs, (c) 1108 fs, (d) 1116 fs, and (e) 1290 fs.

trajectory “skirts” the deep potential energy minimum of the CH2(OH)2‚‚‚F- IRC complex and has non-IRC dynamics reminiscent of those for the OH- + CH3F f CH3OH + Freaction.6 4.1.2. HF + CH3OO- Products and CH3OOH‚‚‚F- Complex. As shown in Table 4, three of the trajectories led to proton transfer from the hydroxyl group and the HF + CH3OOproducts, while three of the CH3OOH‚‚‚F- complexes, formed by the F- + CH3OOH collisions, dissociated to HF + CH2O + OH-. The PES suggests that the HF + CH3OO- product channel should proceed via the CH3OOH‚‚‚F- complex, and since the barrier for this complex to dissociate to HF + CH3OOis 16.4 kcal/mol (see Figure 2) higher than that to dissociate to HF + CH2O + OH-, it is somewhat surprising that there are the same number of events via this complex leading to HF + CH3OO- and to HF + CH2O + OH-. However, visualization J. AM. CHEM. SOC.

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Figure 6. A two-dimensional contour diagram of the post-transition state potential energy surface for TS1. Q1 ) ∆r1 + ∆r2, where r1 is the FH-C bond length and r2 is the O-OH bond length. Q2 ) ∆θ1 + ∆θ2, where θ1 is the O-C-O angle and θ2 is the H-O-C angle; i.e., H is the hydrogen abstracted by F-, and O is the oxygen attached to carbon. Q1 represents the concerted motion of HF and OH- away from CH2O, and Q2 represents rotation of CH2O. The remaining coordinates were optimized for each Q1, Q2 point. Depicted on this contour diagram is the IRC (red line) and a representative trajectory (black line).

of the proton-transfer trajectories to form HF + CH3OO- shows that they are direct-type events and not mediated by a complex with randomization of its energy. For one of the trajectories HF is formed by a direct abstraction. For another the relative motion of F- and the H-atom of H-O-O- reached its inner turning point (ITP) two times, which resulted from rotation as the proton is abstracted. For the third proton-transfer event the potential energy released, as F- approaches the H-O-Ogroup, is localized in the F - - H - - O - moiety, resulting in multiple transfer of the H-atom between the F and O atoms. Proton transfer occurred after there were five ITPs in the F-H relative motion. In contrast, the three dissociations of the CH3OOH‚‚‚F- complex to form the HF + CH2O + OHproducts via the ECO2 mechanism are more consistent with a statistical model. The lifetime of the complex varies from 0.452.1 ps for these three events, and as discussed below, the observation of three dissociations is consistent with RRKM theory. There are several interesting aspects of the dynamics associated with formation of the CH3OOH‚‚‚F- complex. For two of the trajectories, F- approached the H-atom of the H-O-Ogroup but rebounded off to the CH3- group forming HF + CH2O + OH-. For 19 of the trajectories, F- bounced from the CH3- to the H-O-O- group to form the CH3OOH‚‚‚Fcomplex. These latter events are not surprising given the shallowness of the F-‚‚‚CH3OOH potential energy minimum. 4.1.3. Nonreactive Trajectories. 55 of the trajectories were nonreactive and went back to the F- + CH3OOH reactants. For 42 of these trajectories F- moved past CH3OOH, scattering in the forward direction, but for the remaining 13 trajectories Fscattered off CH3OOH. The F- ion hit the CH3- group for 10 of these trajectories and rebounded with one inner turning point (ITP) in the F- + CH3OOH relative motion. One trajectory had similar dynamics, but F- struck the OH- group. Two of the trajectories had a single ITP encounter with both the CH3- and OH- groups. For one F- first struck the CH3- group, and for 9982 J. AM. CHEM. SOC.

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the other F- first struck the OH- group. These trajectories, in which F- scatters nonreactively off the CH3- and OH- groups, would be identified as reactive events in a variational transition state theory analysis of the F- + CH3OOH chemical reaction.28 4.2. Trajectories Initiated at TS1. 80 trajectories were propagated starting at transition state TS1. Microcanonical sampling was used to determine the initial conditions for the trajectories with an energy corresponding to the thermal energy of the reactants plus the potential energy difference between the reactants and the TS1 structure. The reaction coordinate translational energy was sampled from its 300 K Boltzmann distribution. A 300 K rotational energy distribution was also added to TS1, which results in a much lower angular momentum than that created by the F- + CH3OOH reactive collisions. As seen in Table 4, 95% of the trajectories formed HF + CH2O + OH-. The remaining trajectories formed minor products such as HF + CO + H2 + OH-, F- + CO +H2 + H2O, and HF + HCO- + H2O, which were not observed in the collision dynamics simulations discussed above (section 4.1). No evidence for formation of the IRC product was found for the trajectories initiated at TS1. The dynamics of the trajectories forming the primary products HF + CH2O + OH- is similar to that observed for the F- + CH3OOH collision dynamics (Figure 5c-e). As these trajectories moved from TS1 they followed the IRC, including the formation of a tight HF‚‚‚CH2O‚‚‚HO- complex, followed by rotation of the CH2O fragment and rearrangement of the HF and OH- fragments, similar to that for the IRC path at an s of approximately 2-5 amu1/2 Bohr. However, instead of continuing to follow the IRC to form CH2(OH)2‚‚‚F-, the trajectories left the IRC and formed HF, OH-, and CH2O. 4.3. Trajectories Initiated at the HOCH2O-‚‚‚HF Structure on the IRC. Five trajectories were initiated at the HOCH2O-‚‚‚HF structure on the IRC, identified by the dot in Figure 3. Initial conditions were determined using a microcanonical sampling scheme. The energy for the trajectories was determined by adding the thermal energy of the reactants to the potential energy difference between the reactants and the HOCH2O-‚‚‚HF structure. In addition the energies for reaction coordinate translation and external rotation were sampled from their 300 K Boltzmann distributions. The motivation for this simulation was to see if initializing the trajectories far along the IRC, with a potential energy of -67 kcal/mol with respect to TS1, would direct them to the IRC products. However, each of the trajectories formed the HF + CH2O + OH- products with no evidence of following the IRC path. 4.4. RRKM Calculation. Quantum and classical RRKM calculations were performed for dissociation of the CH3OOH‚‚‚Fcomplex via TS2 and TS1 using the B3LYP/6-311+G(d,p) frequencies and energies, the same level of theory used for the direct dynamics simulations. External rotations were treated with the adiabatic symmetric top approximation in calculating the sum and densities of states.29 The total angular momentum was set to the average total angular momentum for the trajectories forming the CH3OOH‚‚‚F- complex. Dissociation of CH3OOH‚‚‚F- to the HF + CH2O + OH- products proceeds through TS2 and TS1, and the statistical rate constant for this process is (28) Truhlar, D. G.; Hase, W. L.; Hynes, J. T. J. Phys. Chem. 1983, 87, 2664. (29) Zhu, L.; Hase, W. L. Chem. Phys. Lett. 1990, 175, 117.

Direct Dynamics of F- + CH3OOH Reactive Collisions

k)

k2k1 k1 + k-2

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(2)

where the rate constants are for the reactions k2

z F-‚‚‚CH3OOH CH3OOH‚‚‚F- y\ k -2

k1

F-‚‚‚CH3OOH 98 products past TS1 It is of interest that the quantum harmonic RRKM value for k1 is ∼10 times larger than the value for k-2, since the barrier for k1 is larger than that for k-2. This is because TS2 has a much “tighter” structure, with higher vibrational frequencies, than does TS1. The quantum harmonic RRKM value for k is 0.0018 ps-1, and the RRKM lifetime τ ) 1/k ) 556 ps. For the 4 ps trajectories, the dynamics of the CH3OOH‚‚‚F- complex is followed on average for 2.3 ps. The RRKM value for the fraction of complexes which dissociate is 1 - exp(-kt) with t ) 2.3 ps. Thus, the RRKM percentage of trajectories which should dissociate is 0.4% and smaller than the 3% value found in our simulations; i.e., of the 100 complexes formed, 3 dissociated via TS2 and TS1 to form HF + CH2O + OH-. Quantum RRKM theory retains a fixed amount of energy in zero-point energy (ZPE) for both the reactants and TS. However, classical dynamics does not necessarily preserve ZPE,30,31 and if the classical intramolecular dynamics is ergodic the ZPE flows freely between the vibrational degrees of freedom of the decomposing molecule and TS. Thus, the barrier for decomposition is the classical potential energy barrier. The classical harmonic RRKM rate constant is larger than the quantum value,32 and for CH3OOH‚‚‚F- decomposition the classical harmonic RRKM rate constant k is 0.0155 ps-1 and 8.6 times larger than the quantum value. The percentage of the complexes predicted to decompose is 3.5% and in remarkably good agreement with the trajectory result of 3%. However, better trajectory statistics are needed to make this comparison more definitive. It is also possible there is an apparent non-RRKM33 component in the dissociation of CH3OOH‚‚‚F-. An important approximation in the RRKM calculations is the assumption of harmonic energy levels for both CH3OOH‚‚‚Fand the transition states. Because the vibrational energy of CH3OOH‚‚‚F- is higher than that of the transition states, the anharmonic correction is expected to be more important for the CH3OOH‚‚‚F- density of states than the transition states sums of states. As a result, anharmonicity will decrease the rate constant by increasing the density of states. An anharmonic correction may be particularly important for the intermolecular degrees of freedom of CH3OOH‚‚‚F-, which represent the interaction of F- with CH3OOH.34 Anharmonic effects are often important,4 and it is noteworthy, that for a recent direct dynamics simulation of molozonide dissociation, an anharmonic correction of 2.2-2.6 was suggested.35 (30) (31) (32) (33) (34) (35)

Lu, D.; Hase, W. L. J. Chem. Phys. 1988, 89, 6723. Miller, W. H.; Hase, W. L.; Darling, C. L. J. Chem. Phys. 2006, 91, 2863. Hase, W. L.; Buckowski, D. G. J. Comput. Chem. 1982, 3, 335. Bunker, D. L.; Hase, W. L. J. Chem. Phys. 1973, 59, 4621. Peslherbe, G. H.; Wang, H.; Hase, W. L. J. Chem. Phys. 1995, 102, 5626. Vayner, G.; Addepalli, S. V.; Song, K.; Hase, W. L. J. Chem. Phys. 2006, 125, 14317.

4.5. Comparison with Experiment. The dynamics of the F- + CH3OOH reaction has been studied in previous experiments at 300 K utilizing a tandem flowing afterglow-selected ion flow tube (FA-SIFT) mass spectrometer.18 The measured rate constant is k ) 1.23 × 10-9 cm3/molecule‚s, and the major primary product is OH-. A minor complication in determining the relative importance of the product channels is that OHundergoes a secondary reaction with CH3OOH to form H2O + CH3OO-. This latter ion is also formed by F- + CH3OOH direct proton transfer. The importance of the OH- + CH3OOH secondary reaction was unraveled by studying it separately. A numerical analysis of the experimental data, for F- + CH3OOH and OH- + CH3OOH, suggests that the reaction of F- with CH3OOH proceeds mainly via the formation of OH- (∼85%) with an upper bound for direct proton transfer to form CH3OOestimated to be approximately 10%.18 An ECO2 mechanism was proposed for OH- formation from the experimental results.18 In this mechanism deprotonation from the R-carbon, by the attacking anion, leads to carbon-oxygen double bond formation with concerted elimination of the anionic leaving group. For the F- + CH3OOH reaction, the products of the ECO2 mechanism are HF + CH2O + OH-. Supporting evidence for the ECO2 mechanism comes from studying the kinetics of the reverse reaction, CH3OO- + HF. Measurements with the FA-SIFT technique gives a rate constant of k ) 2.43 × 10-9 cm3/molecule‚s and identifies, with 81% yield, OH- as the primary reaction product. The proposal, based in part on ab initio calculations, is that the reactants form the F-‚‚‚CH3OOH complex which then dissociates via the ECO2 mechanism to form HF + CH2O + OH-. The F- + CH3OOH direct dynamics simulations reported here are in excellent agreement with the experimental measurements and the mechanistic details suggested from the experiments. The simulations identify the same ECO2 mechanism for OH- formation (see Figure 5) as proposed from the experiments. The direct dynamics rate constant is given by the expression k ) 〈Vrel〉 σrxn, where 〈Vrel〉 is the relative velocity for the average translational energy 3RT/2 ) 0.89 kcal/mol at 300 K and σrxn is the reaction cross section, and is given by Prxnπ b2max, where Prxn is the reaction probability and the fraction of trajectories that react. From Table 4 Prxn ) 145/200 ) 0.73 ( 0.03. For bmax ) 10 Å used in the simulations (see section 3.2), the resulting σrxn is 229 ( 10 Å2, so that k ) (1.70 ( 0.07) × 10-9 cm3/molecule‚s and in quite good agreement with the experimental value 1.23 × 10-9 cm3/molecule‚s. A direct comparison cannot be made with the ∼85% and ∼10% branching found from the experiments for the HF + CH2O + OH- and HF + CH3OO- product channels, since a large number of CH3OOH‚‚‚F- complexes remain undissociated when the trajectories are terminated at 4 ps (see Table 4). However, if these complexes are assumed to dissociate statistically as predicted by RRKM, nearly all will form the HF + CH2O + OH- products since the barrier is 16.4 kcal/mol lower for this channel. With this assumption, the branching between the HF + CH2O + OH- and HF + CH3OO- product channels is predicted to be 142/145 ) 0.98 ( 0.01 and 3/145 ) 0.02 ( 0.01, fractions in qualitative agreement with the experimental results. The experimental estimates of approximately 85% and 10% for these two channels are based on a difficult numerical analysis that subtracted a large contribution from the secondary J. AM. CHEM. SOC.

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reaction OH- + CH3OOH f CH3OO- + H2O.36 Thus, the trajectory estimate of only ∼2% branching to the HF + CH3OO- products is not inconsistent with the experiments. The finding from the simulation, that none of the trajectories followed the IRC to form the CH2(OH)2‚‚‚F- complex, is also consistent with the experimental study.18 If formed, the complex will contain ∼110 kcal/mol of internal energy and is expected to undergo substantial dissociation to both HF + CH2(OH)Oand F- + CH2(OH)2, since the channels have barriers of only ∼40-45 kcal/mol. The former dissociation channel was searched for in the experiments by studying the F- + CD3OOH reaction, for which formation and dissociation of the IRC complex would give DF + CD2(OH)O-. The proton transfer anion CD3OOwas observed, but the IRC product ion CD2(OH)O- was not, indicating there was at most only a very small number of events which followed the IRC. A minor product with a 2% yield and corresponding to the mass of F- + CH3OOH was detected. Presumably this percentage corresponds to undissociated CH3OOH‚‚‚F- complexes. It also sets an upper bound on the amount of the IRC complex produced. The most likely scenario is that the formation of the IRC complex is negligibly small (